Depositing Arced Portions of Fiber-Reinforced Thermoplastic Filament

ABSTRACT

A technique for depositing fiber-reinforced thermoplastic filament in an arc is disclosed that mitigates the centripetal forces that arise in the prior art. In accordance with the illustrative embodiment, the centripetal forces are ameliorated by twisting the filament while depositing it in an arc.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is related to “Alleviating Torsional Forces onFiber-Reinforced Thermoplastic Filament,” application Ser. No.15/______, Attorney Docket 3019-143us1, which is incorporated byreference herein in its entirety.

FIELD OF THE INVENTION

The present invention relates to 3D printing in general, and, moreparticularly, to the deposition of fiber-reinforced thermoplasticfilament.

BACKGROUND

In general, there are two complementary techniques for manufacturing anobject: additive manufacturing and subtractive manufacturing.

Additive manufacturing involves aggregating material to form the desiredobject. In contrast, subtractive manufacturing involves removingmaterial to form the desired object. In practice, many objects aremanufactured using a combination of additive and subtractive techniques.

A form of additive manufacturing—colloquially known as“three-dimensional (3D) printing”—is the subject of intense research anddevelopment because it enables objects with complex geometries to bemanufactured without molds or dies. Furthermore, 3D printing enables themass customization of objects with different dimensions andcharacteristics. There remain, however, many challenges in the design,manufacture, and use of 3D printers.

SUMMARY OF THE DISCLOSURE

The present invention provides a mechanism for depositing arced portionsof fiber-reinforce thermoplastic filament without some of the costs anddisadvantages for doing so in the prior art.

In accordance with the illustrative embodiment of the present invention,a 3D printing system manufactures an object by depositing one or moresegments of fiber-reinforced thermoplastic filament in a prescribedorder and geometry.

The thermoplastic filament is approximately cylindrical and comprises alongitudinal axis L. The filament, as manufactured, comprises aplurality of continuous carbon-fibers that are substantially parallelwith the longitudinal axis L of the filament.

Thermoplastic filament is manufactured and stored on spools in very longcontinuous lengths (e.g., hundreds of meters, thousands of meters, tensof thousands of meters, etc.). At the time of printing, the filament isunspooled and cut into distinct segments. The segment has a length sthat is measured along the longitudinal axis L.

The filament, as manufactured, is neither pliable nor adhesive atstandard pressure and temperature. During deposition, a small portion ofa segment of filament is heated to make it pliable and adhesive and thenthe heated portion is guided and pressed into position where it coolsand solidifies.

Each segment, as deposited, comprises:

(i) one or more straight (i.e., rectilinear) portions, or

(ii) one or more non-straight (i.e., curved) portions, or

(iii) any combination of i and ii.

As will be clear to those skilled in the art, every curved portion intwo- and three-dimensions can be approximated by a combination of arcedportions.

When a portion of a segment of filament is deposited in an arc, thefibers on the “outside” of the arc—which have a high-tensile strengthand do not stretch—effectively experience a centripetal force that dragsthem—and the thermoplastic with which they are impregnated—towards thecenter of the arc. This inhibits the adhesion of the filament to theunderlayment and causes the thermoplastic to form clumps.

The illustrative embodiment alleviates the centripetal force associatedwith depositing fiber-reinforced thermoplastic filament in arcedportions by twisting the filament while it is deposited in an arc. Inaccordance with the illustrative embodiment, a portion of a segment offilament of length s that is deposited in an arc of θ radians with aradius R, is twisted φ radians around the longitudinal axis L, where:

φ=2πN   (Eq. 1)

where N is a non-zero integer (e.g., +1, −1, etc.) It is worth notingthat the amount of twist φ is independent of θ and independent of theradius R, although it will be clear to those skilled in the art, afterreading this disclosure, to only twist the filament for arcs in which θexceeds a threshold (e.g.,

$\left. {\frac{\pi}{12},\frac{\pi}{24},\frac{\pi}{36},{{etc}.}} \right)$

or the radius R exceeds a (e.g., two times the diameter of the filament,three times the diameter of the filament, etc.) or in which both θexceeds a threshold and the radius R exceeds a threshold.

For context, when fibers are not twisted around the longitudinal axis L,

${\frac{d\; \phi}{ds} = 0},$

and when the fibers are twisted around the longitudinal axis L,

$\frac{d\; \phi}{ds} \neq 0.$

In accordance with the illustrative embodiment, the rate of twist in anarced portion of a segment of filament is constant (i.e.,

$\left. {\frac{d^{2}\phi}{{ds}^{2}} = 0} \right).$

In accordance with the illustrative embodiment, the portion of thefilament to be twisted is twisted by an actuator at the deposition head.The twisting of the filament at the deposition head creates torsionalforces on both the “downstream” portion of the filament (i.e., thelength of filament between the deposition head and the point ofdeposition on the workpiece) and on the “upstream” portion of thefilament (i.e., the length of filament between the deposition head andthe spool of filament).

The torsional forces on the downstream filament are desirable becausethey cause the twisting of the filament which is permanently fixed intothe object of manufacture. In contrast, the torsional forces on theupstream filament are reactive and serve no purpose and must bealleviated to prevent the upstream filament from shearing and breaking.

In accordance with the illustrative embodiment, there are three ways ofalleviating the torsional forces on the upstream filament.

First, the upstream filament and the spool of filament itself can betwisted φ radians around the longitudinal axis L of the upstreamfilament. It will be clear to those skilled in the art, after readingthis disclosure, how to make and use machinery for accomplishing this.

Second, each twist of +φ radians in one arced portion of filament can befollowed by a twist of −φ radians in the next arced portion, and eachtwist of −φ radians in one arced portion of filament could be followedby a twist of +φ radians in the next arced portion. If the upstreamfilament does not break when twisted φ radians, then this approach hasthe advantage of placing a limit on the torsional force. Furthermore,the maximum force can be distributed along a long unspooled length ofupstream filament.

Third, a portion of the upstream filament can be heated above the glasstransition temperature T_(g) of the thermoplastic, which allows thethermoplastic molecules to realign themselves in response to thetorsional force. This is akin to annealing and has the advantage ofeliminating the internal torsional forces in the thermoplastic.

The illustrative embodiment comprises:

method of depositing a thermoplastic filament that comprises (i) alongitudinal axis L and (ii) a reinforcing fiber that is substantiallyparallel to the longitudinal axis L, the method comprising:

depositing a first portion of a segment of the thermoplastic filament ina straight line without twisting the thermoplastic filament around thelongitudinal axis L and without twisting the reinforcing fiber aroundthe longitudinal axis L, wherein the first straight portion of thesegment has a length of S₁ as measured along the longitudinal axis L;and

depositing a second portion of the segment of the thermoplastic filamentin a first arc of θ₁ radians and radius R₁ while twisting thethermoplastic filament and the reinforcing fiber φ₁ radians around thelongitudinal axis L, wherein the second arced portion of the segment hasa length of S₂ as measured along the longitudinal axis L; and

depositing a third portion of the segment of the thermoplastic filamentin a straight line without twisting the thermoplastic filament aroundthe longitudinal axis L and without twisting the reinforcing fiberaround the longitudinal axis L, wherein the third portion of the segmenthas a length of S₃ as measured along the longitudinal axis L;

wherein the first portion of the segment and the second portion of thesegment are contiguous; and

wherein the second portion of the segment and the third portion of thesegment are contiguous;

wherein S₁, S₂, S₃, and R₁ are positive real numbers, and wherein θ₁ andφ₁ are real numbers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an illustration of the salient components of additivemanufacturing system 100 in accordance with the illustrative embodimentof the present invention.

FIG. 2 depicts an illustration of deposition head 122, which includestwisting device 210.

FIG. 3 depicts an illustration of the spatial relationship of thesalient components of deposition head 122 to a previously-depositedsegment of thermoplastic filament 131.

FIG. 4 depicts an illustration of filament conditioning unit 129, whichincludes heating device 401.

FIG. 5 depicts a block diagram of the salient components of controller101.

FIG. 6A through 6C depict a flowchart of at least some of the salientprocesses performed in accordance with the illustrative embodiment ofthe present invention.

FIG. 7 depicts a side view of segment 701 of thermoplastic filament 131.

FIG. 8 depicts a cross sectional view of segment 701 of thermoplasticfilament 131 in relation to longitudinal axis 702.

FIG. 9 depicts a first portion, a second portion, and a third portion ofsegment 701 of filament 131.

FIG. 10 depicts a first straight portion, a first arced portion, asecond arced portion, and a second straight portion of segment 701 offilament 131.

DEFINITIONS

Arc—for the purposes of this specification, the term “arc” and itsinflected forms is defined as a non-zero part of a circle.

Curve—for the purposes of this specification, the term “curve” and itsinflected forms is defined as a curvilinear path that comprises one ormore contiguous segments, wherein at least one segment is an arc.

Straight line—for the purposes of this specification, the term “straightline” and its inflected forms is defined as a rectilinear path.

DETAILED DESCRIPTION

The techniques of the illustrative embodiment are described in thisspecification in the context of handling thermoplastic filamentcomprising fibers, in an additive manufacturing system. As those who areskilled in the art will appreciate after reading this specification, thedisclosed techniques can also be used in various other applications, andwith either filaments or other slender threadlike objects or fibers.

Furthermore, the techniques of the illustrative embodiment are describedin this specification in the context of twisting a portion of thefilament in response to a bending of the portion. As those who areskilled in the art will appreciate after reading this specification, thedisclosed techniques can also be used for twisting a portion of thefilament in response to a different type of force that is applied to theportion than bending, such as tension, compression, shear, or torsion(twisting) that is different from the twisting that is provided inresponse.

FIG. 1 depicts an illustration of the salient components of additivemanufacturing system 100 in accordance with the illustrative embodimentof the present invention. Additive manufacturing system 100 comprises:controller 101, build chamber 102, turntable 110, deposition build plate111, robot 121, deposition head 122, filament conditioning unit 129,filament source 130, and thermoplastic filament 131. A purpose ofmanufacturing system 100 is to manufacture object 151, which can be anarticle of manufacture or at least part of an apparatus.

Controller 101 comprises the hardware and software necessary to directbuild chamber 102, robot 121, deposition head 122, and turntable 110, inorder to manufacture object 151. The controller also directs at leastsome of the components that are part of deposition head 122, asdescribed below. Controller 101 comprises computer-aideddesign/computer-aide manufacturing (CAD/CAM) functionality in order tocontrol the aforementioned components. Controller 101 is described belowand in regard to FIG. 5.

Build chamber 102 is a thermally-insulated, temperature-controlledenvironment in which object 151 is manufactured. It will be clear tothose skilled in art how to make and use build chamber 102.

Turntable 110 comprises a stepper motor under the control of controller101 that is capable of rotating build plate 111 (and, consequentlyobject 151) around the Z-axis (i.e., orthogonal to the build plate). Inparticular, turntable 110 is capable of:

-   -   i. rotating build plate 111 clockwise around the Z-axis from any        angle to any angle, and    -   ii. rotating build plate 111 counter-clockwise around the Z-axis        from any angle to any angle, and    -   iii. rotating build plate 111 at any rate, and    -   iv. maintaining (statically) the position of build plate 111 at        any angle.

In some embodiments of the present invention, turntable 110 is furthercapable of being positioned in general (i.e., not being limited torotation around the Z-axis), under the control of controller 101, andaccordingly is sometimes referred to as a “build plate positioner.”Itwill be clear to those skilled in the art how to make and use turntable110.

Build plate 111 is a platform comprising hardware on which object 151 ismanufactured. Build plate 111 is configured to receive heated filamentdeposited by deposition head 122.

As those who are skilled in the art will appreciate, build plate 111need not be coupled to a turntable, in order for it to receive theheated filament. In any event, it will be clear to those skilled in theart how to make and use build plate 111.

Robot 121 is capable of depositing a run of material, via depositionhead 122, from any three-dimensional coordinate in build chamber 102 toany other three-dimensional coordinate in build chamber 102 withdeposition head 122 at any approach angle. To this end, robot 121comprises a multi-axis (e.g., six-axis, seven-axis, etc.), mechanicalarm that is under the control of controller 101. The mechanical armcomprises first arm segment 123, second arm segment 124, and third armsegment 125. The joints between adjoining arm segments are under thecontrol of controller 101. A non-limiting example of robot 121 is theIRB 4600 robot offered by ABB. It will be clear to those skilled in theart how to make and use robot 121.

The mechanical arm of robot 121 can move roller 204 of deposition head122, described below and in FIG. 2, in:

-   -   i. the +X direction,    -   ii. the −X direction,    -   iii. the +Y direction,    -   iv. the −Y direction,    -   v. the +Z direction,    -   vi. the −Z direction, and    -   vii. any combination of i, ii, iii, iv, v, and vi,

while rotating the approach angle of the roller around any point ortemporal series of points. It will be clear to those skilled in the arthow to make and use robot 121.

Deposition head 122 comprises hardware that is under the control ofcontroller 101 and that deposits filament 131, which may partially orwholly contain one or more fiber strands. Deposition head 122 isdescribed below and in regard to FIG. 2. Deposition head 122 is anexample of an “end effector” in relation to robot 121, being attached torobot 121 at the robot's wrist.

Filament conditioning unit 129 comprises hardware that is under thecontrol of controller 101 and that conditions filament 131. Unit 129 isattached to robot 121 at arm segment 124. As those who are skilled inthe art will appreciate after reading this specification, unit 129 canbe attached to a different arm segment, or to something other than robot121 entirely (e.g., deposition head 122, etc.). Filament conditioningunit 129 is described below and in regard to FIG. 4.

Thermoplastic filament 131 comprises a longitudinal axis L, depicted inFIGS. 7 through 10, and a reinforcing fiber that is substantiallyparallel to the longitudinal axis. In accordance with the illustrativeembodiment, thermoplastic filament 131 comprises a cylindrical towpregof contiguous 12K carbon fiber that is impregnated with thermoplasticresin and is supplied from filament source 130 (e.g., a spool, etc.).Thermoplastic filament 131 comprises contiguous carbon fiber, but itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which thermoplastic filament 131 has a different fibercomposition.

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which filament 131 comprises a different number of fibers(e.g., 1K, 3K, 6K, 24K, etc.). It will be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which the fibers in filament 131are made of a different material (e.g., fiberglass, aramid, carbonnanotubes, etc.).

In accordance with the illustrative embodiment, the thermoplastic is, ingeneral, a semi-crystalline polymer and, in particular, thepolyaryletherketone (PAEK) known as polyetherketone (PEK). In accordancewith some alternative embodiments of the present invention, thesemi-crystalline material is the polyaryletherketone (PAEK),polyetheretherketone (PEEK), polyetherketoneketone (PEKK),polyetheretherketoneketone (PEEKK), or polyetherketoneetherketoneketone(PEKEKK). As those who are skilled in the art will appreciate afterreading this specification, the disclosed annealing process, as itpertains to a semi-crystalline polymer in general, takes place at atemperature that is above the glass transition temperature Tg.

In accordance with some alternative embodiments of the presentinvention, the semi-crystalline polymer is not a polyaryletherketone(PAEK) but another semi-crystalline thermoplastic (e.g., polyamide (PA),polybutylene terephthalate (PBT), poly(p-phenylene sulfide) (PPS), etc.)or a mixture of a semi-crystalline polymer and an amorphous polymer.

When the filament comprises a blend of an amorphous polymer with asemi-crystalline polymer, the semi-crystalline polymer can one of theaforementioned materials and the amorphous polymer can be apolyarylsulfone, such as polysulfone (PSU), polyethersulfone (PESU),polyphenylsulfone (PPSU), polyethersulfone (PES), or polyetherimide(PEI). In some additional embodiments, the amorphous polymer can be, forexample and without limitation, polyphenylene oxides (PPOs),acrylonitrile butadiene styrene (ABS), methyl methacrylate acrylonitrilebutadiene styrene copolymer (ABSi), polystyrene (PS), or polycarbonate(PC). As those who are skilled in the art will appreciate after readingthis specification, the disclosed annealing process, as it pertains to ablend of an amorphous polymer with a semi-crystalline polymer, takesplace generally at a lower temperature than a semi-crystalline polymerwith the same glass transition temperature; in some cases, the annealingprocess can take place at a temperature slightly below the glasstransition temperature.

When the filament comprises a blend of an amorphous polymer with asemi-crystalline polymer, the weight ratio of semi-crystalline materialto amorphous material can be in the range of about 50:50 to about 95:05,inclusive, or about 50:50 to about 90:10, inclusive. Preferably, theweight ratio of semi-crystalline material to amorphous material in theblend is between 60:40 and 80:20, inclusive. The ratio selected for anyparticular application may vary primarily as a function of the materialsused and the properties desired for the printed object.

In some alternative embodiment of the present invention, the filamentcomprises a metal. For example, and without limitation, the filament canbe a wire comprising stainless steel, Inconel® (nickel/chrome),titanium, aluminum, cobalt chrome, copper, bronze, iron, precious metals(e.g., platinum, gold, silver, etc.).

Thermoplastic filament 131 is deposited as a “run of material” ontoobject 151 or build plate 111, or both. For purposes of clarity,however, filament 131 is depicted in FIG. 1 as being not in contact withobject 151. The particular shape of object 151 as depicted has beenselected for pedagogical purposes, but additive manufacturing system 100is capable of building any of a variety of objects.

FIG. 2 depicts an illustration of deposition head 122. Deposition head122 comprises: mount 201, filament guide 202, filament guide support203, roller 204, deposition head body 205, laser 206, laser support 207,filament drive 208, conduit 209, and twisting device 210, interconnectedas shown. As those who are skilled in the art will appreciate afterreading this specification, one or more of the elements that aredepicted as being part of deposition head 122 can instead be part ofrobot 121 or a different part of additive manufacturing system 100.

In accordance with the illustrative embodiment, the relative spatialpositions of mount 201, filament guide 202, support 203, roller 204,deposition head body 205, laser 206, support 207, filament drive 208,and twisting device 210 are invariant, but it will be clear to thoseskilled in the art, after reading this disclosure, in which the relativespatial positions of two or more of them is not invariant.

Mount 201 of deposition head 122 comprises one or more parts that areconfigured to mount the other components of deposition head 122 to thearm of robot 121.

Filament guide 202 is configured to guide filament 131, toward adeposition surface at a deposition point, in accordance with theillustrative embodiment. In some embodiments of the present invention,at least a portion of filament guide 202 is transparent—or substantiallytransparent—to the light from laser 206 so that the laser can add heatto filament 131 while filament 131 is within filament guide 202. Anexample of filament guide 202 is provided in co-pending U.S. applicationSer. No. 15/827,721, entitled “Filament Guide,” filed on Nov. 30, 2017(Attorney Docket: 3019-142us1), which is incorporated by referenceherein and for the purposes of disclosing how filament guide 202 is madeand used in conjunction with the deposition of heated filaments ofthermoplastic. The filament guide is attached to mount 201 via support203.

Roller 204 is a metal wheel with roller bearings on an axle. In order todeposit filament 131, roller 204 is configured to apply a pressing forcebetween i) filament 131, when heated, and ii) a deposition surface,which can be a surface of build plate 111 or a surface of object 151.Roller 204 is attached to mount 201 via body 205, which positions theroller, and is rotatably coupled to body 205 via the axle. In someembodiments of the present invention, body 205 is attached to mount 201via an intermediate support member.

In accordance with the illustrative embodiment, roller 204 rotatesfreely on its roller axle and presses filament 131 intopreviously-deposited filament 151 (i.e., the object being manufactured).Filament 131 is pressed into previously-deposited filament 151 tofacilitate adhesion and eliminate voids. The pressing force is generatedvia the arm of robot 121, as controlled by controller 101.

Laser 206, as a heating device, is a heat source configured to heatfilament 131 while the filament is moving through guide 202. Laser 206is configured to emit electromagnetic radiation in the form of infraredlight. In some alternative embodiments of the present invention, thelaser emits electromagnetic radiation in a different form, while in someother embodiments laser 206 is instead a heat source other than a laser,or emits thermal energy that which might be in a form other thanelectromagnetic radiation, or both. Laser 206 is attached to mount 201via support 207.

The particular source of the heat is sufficient to heat thethermoplastic in a length of filament 131 prior to the length reachingthe deposition point, for each such length of filament. When heated inthis way by laser 206, the thermoplastic in the filament becomes pliableand adhesive, and can be pressed and deposited by roller 204. The laseris configured to produce a temperature at filament 131 that is highenough to make the thermoplastic pliable and adhesive, but not too high.If the thermoplastic is too cool, it is not sufficiently pliable oradhesive, and if the thermoplastic is too hot, it melts and itsviscosity becomes too low.

In some embodiments of the present invention, laser 206 is a LaserlineLDM-800 diode laser that heats both a length of a segment of filament131 and a length of a segment of previously-deposited filament 151 underthe control of controller 101. It will be clear to those skilled in theart, after reading this disclosure, how to make alternative embodimentsof the present invention that use a different laser.

Filament drive 208 is configured to feed filament 131 at a non-zero feedvelocity controlled by controller 101. Drive 208 feeds the filamentforward along the longitudinal axis of the filament, in particulartoward and through filament guide 202 and other components. The feedvelocity is important in regard to design considerations of filamentguide 202 as described below, as well as in regard to other reasons. Insome embodiments of the present invention, drive 208 is attached tomount 201 via its own support member.

Conduit 209 is configured to provide a predetermined gas from a sourceof the gas to filament guide 202, in particular to filament 131 withinguide 202. In some embodiments of the present invention, the gas that isused has properties enabling it to displace oxygen such that combustionis inhibited when filament 131 is heated by laser 206. For example andwithout limitation, the predetermined gas can be nitrogen. Conduit 209is connected to filament guide 202 as described below.

Twisting device 210 comprises a mechanism that is configured to twistfilament 131 around the longitudinal axis of the filament. Device 210twists filament 131 by applying an amount of torque to the filament asneeded and under the control of controller 101. Device 210 is capable oftwisting filament 131 while the filament is moving toward the depositionpoint.

In accordance with the illustrative embodiment, twisting device 210 issituated downstream along filament 131 in relation to filament drive208. In some embodiments in which twisting device 210 is situateddownstream, filament drive 208 is capable of swiveling freely such thatfilament 131 rotates freely around its longitudinal axis while beingsupplied by drive 208. In some other embodiments of the presentinvention, twisting device 210 is instead integrated into filament drive208, wherein a drive mechanism drives filament 131 along thelongitudinal axis of the filament while twisting the filament around thelongitudinal axis.

When a portion of a segment of filament 131 is twisted by twistingdevice 210, including its reinforcing fibers, the twisted portion of thefilament can then be deposited as an arced portion by deposition head122, in a manner that mitigates the forces exerted on the fibers as aresult of bending them.

In some embodiments of the present invention, when a portion of asegment of filament 131 is twisted by twisting device 210, filamentsource 130 can rotate accordingly, in order to accommodate the twistthat is imparted to filament 131, and while under the control ofcontroller 101. As those who are skilled in the art will appreciateafter reading this specification, the amount of rotation of filamentsource 130 and the timing of the rotations can depend on variousconsiderations. These considerations include i) the amount of rotationof each filament portion, ii) the timing of the rotations of thefilament portions, iii) the directions of the rotations of a series offilament portions to be rotated, and iv) the amount of slack maintainedin filament 131 between filament source 130 and twisting device 210, forexample and without limitation. The total accumulated amount of rotationin any one direction (i.e., counterclockwise or clockwise) of filamentsource 130 can be minimized, for example, by controller 101 keepingtrack of the direction of rotation of each filament portion, asdescribed below and in FIG. 6B.

FIG. 3 depicts an illustration of the spatial relationship of thesalient components of deposition head 122 to one or more previouslydeposited segments of thermoplastic filament 131 that constitute object151. In accordance with the illustrative embodiment, the salientcomponents of deposition head 122 comprise: filament guide 202, support203, roller 204, deposition head body 205, laser 206, and twistingdevice 210.

For the purposes of this specification, deposition point 322, bydefinition, is always “under” the roller at the point or area ofdeposition, as opposed to being at a fixed point or area on build plate111 or object 151. Deposition point 322 is associated with surface 321.

Deposition head 122 is capable of depositing one or more portions of oneor more segments of filament 131 in a straight line without twisting thethermoplastic filament and without twisting the reinforcing fiber in thefilament around the filament's longitudinal axis. Deposition head 122deposits portions in a straight line along the direction of travelindicated in FIG. 3, with respect to a fixed point on build plate 111.

Deposition head 122 is also capable of depositing one or more portionsof one or more segments of filament 131 according an arc of angle θ inrelation to a straight line such as the direction of travel indicated inFIG. 3, whenever it is determined that such a bend is to be introduced,based on a model of object 151 stored and act on by controller 101. Inparticular, deposition head 122 is capable of depositing one or moreportions of one or more segments of thermoplastic filament 131 accordingto an arc of θ radians and radius R while twisting the thermoplasticfilament and the reinforcing fiber φ radians around the longitudinalaxis of the filament. As those who are experienced in the art willappreciate after reading this specification, any type of bend can berepresented as one or more arc portions, wherein each arc portion i isof θ_(i) radians, radius R_(i), and length S_(i) along its longitudinalaxis.

Deposition head 122 is capable of depositing the aforementioned straightportions and arced portions of one or more segments of filament 131, inany combination of straight and/or arced portions, and in which anycombination of portions can be contiguous with respect to one another.

FIG. 4 depicts an illustration of filament conditioning unit 129.Filament conditioning unit 129 comprises: heating device 401 and coolingsection 402, interrelated as shown. Filament 131 passes through heatingdevice 401 and cooling section 402, in the direction indicated by thearrow and at a feed velocity determined by filament drive 208. As thosewho are skilled in the art will appreciate after reading thisspecification, one or both of the elements that are depicted as beingpart of filament conditioning unit 129 can instead be attached to orassociated with a part of additive manufacturing system 100 differentthan robot arm segment 124.

When heated by heating device 401 and subsequently cooled by coolingsection 402, as described below, the thermoplastic in the filament isannealed as a result, thereby conditioning the thermoplastic that istwisted by twisting device 210.

Heating device 401 is a heat source configured to heat filament 131 inorder to condition the filament for twisting. In accordance with theillustrative embodiment, heating device 401 is a laser similar to laser206 and is configured to emit electromagnetic radiation in the form ofinfrared light. In some alternative embodiments of the presentinvention, the heating device emits electromagnetic radiation in adifferent form, while in some other embodiments the heating device isinstead a heat source other than a laser, or emits thermal energy thatwhich might be in a form other than electromagnetic radiation, or both.Heating device 401 is capable of being controlled by controller 101.

Cooling section 402 provides for the necessary cooling of a heatedportion of filament 131, as part of the annealing process. In accordancewith the illustrative embodiment, cooling section 402 amounts to asufficient distance that separates heating device 401 and twistingdevice 210, such that annealing occurs while concurrently managing(e.g., reducing, avoiding, etc.) internal stresses otherwise introducedby the twisting. The separation is sufficient to provide for passivecooling of each heated portion as the filament moves according to itsfeed velocity. In some embodiments of the present invention, coolingsection 402 can be a device that actively cools each heated portion.

The cooling process represented by cooling section 402 is capable ofbeing controlled by controller 101. The controller can provide control,for example, in adjusting the feed velocity in the case of passivecooling or, for example, in directly adjusting the amount of cooling inthe case of active cooling.

As part of the annealing process, the particular source of heat indevice 401 is sufficient to heat the thermoplastic in a portion offilament 131 prior to the portion being twisted by twisting device 210,for each such portion of filament. The particular source of the heat ofheating device 410 is sufficient to heat, at least to the glasstransition temperature, Tg, each portion of filament 131 to be twisted,such that the portion is at the appropriate temperature when twisted bytwisting device 210. The appropriate temperature is dependent on theparticular thermoplastic being used; in some embodiments of the presentinvention, this temperature is at the annealing temperature as describedearlier, while in some other embodiments this temperature is above theannealing temperature.

In some embodiments of the present invention, the amount of heatprovided by device 410 can be based on other factors as well. Forexample and without limitation, the amount of heat is dependent on theangular amount of twist, φ.

In any event, the temperature of each heated portion of filament 131 hasto be at a point at which torsion forces that would otherwise beintroduced by twisting the filament are avoided or, at least, reduced.Heating device 401 is configured to produce a temperature in thethermoplastic of the filament that is higher than the glass transitiontemperature of the thermoplastic, at least for semi-crystallinepolymers, but not so high such that the filament melts and its viscositybecomes too low.

In some embodiments of the present invention, filament conditioning unit129 heats some or all of filament 131, regardless of whether eachparticular portion of the filament is to be twisted by twisting device210 or not.

FIG. 5 depicts a block diagram of the salient components of controller101. Controller 101 comprises: receiver and transmitter 501, processor502, and memory 503, which are interconnected as shown. In someembodiments of the present invention, controller 101 is a personalcomputer, while in some other embodiments controller 101 is a servercomputer, while in still some other embodiments controller 101 is adifferent type of computing device that is capable of interfacing withand controlling one or more controllable devices.

Receiver and transmitter 501 enables controller 101 to transmit signalsto and receive signals from build chamber 102, turntable 110, robot 121,deposition head 122, and filament conditioning unit 129, including theindividual components thereof. It will be clear to those skilled in theart how to make and use receiver and transmitter 501.

Processor 502 is a general-purpose processor that can execute anoperating system, as well as the application software that performs thetasks described herein and shown in FIG. 6, and of initializing, using,and managing a database representing build parameters of object 151. Itwill be clear to those skilled in the art how to make and use processor502.

Memory 503 is a non-transitory, non-volatile memory that stores:

-   -   i. operating system 511, and    -   ii. application software 512, and    -   iii. the build-parameters database in database 513, as part of a        computer model of object 151.

It will be clear to those skilled in the art how to make and use memory503.

FIGS. 6A through 6C depict a flowchart of at least some of the salientprocesses performed in accordance with the illustrative embodiment ofthe present invention. It will be clear to those having ordinary skillin the art, after reading the present disclosure, how to make and usealternative embodiments of method 600, as well as the other methodsdisclosed in this specification, wherein the recited operationssub-operations, and messages are differently sequenced, grouped, orsub-divided—all within the scope of the present disclosure. It will alsobe clear to those skilled in the art, after reading the presentdisclosure, how to make and use alternative embodiments of the disclosedmethods wherein some of the described operations, sub-operations, andmessages are optional, or are omitted.

Controller 101 either performs each depicted and described operationitself or directs the appropriate component to perform the operation, asdescribed below. As those who are skilled in the art will appreciateafter reading the present disclosure, some alternative embodiments ofthe disclosed operations are performed by components other than thosethat are described below.

At operation 601 of FIG. 6A, controller 101 receives a computer model ofobject 151. In some embodiments of the present invention, the computermodel is based on the object being manufactured from thermoplasticfilament. The computer model is representative of one or more portionsof one or more segments of filament 131 being used to manufacture object151. Controller 101 stores the computer model into memory 503.

The operations that follow are performed for each portion i of a segmentof filament 131, beginning with the first portion (i.e., i equal to 1 asinitialized in operation 602) of the segment, wherein the segmentconsists of I portions. As those who are skilled in the art willappreciate after reading this specification, the operations describedbelow can be repeated for each successive segment of filament 131.

At operation 603, controller 101 determines, based on the storedcomputer model, whether a bend (or curve) having non-zero angle θ is tobe introduced in portion i of thermoplastic filament 131 while beingdeposited on object 151, wherein the portion has a first end and asecond end. In some embodiments of the present invention, the first endof portion i is defined as where the filament is to begin to deviatefrom a straight line in accordance with the bend (i.e., where the bendbegins), and angle θ is measured from the first end. In some embodimentsof the present invention, the second end of portion i is defined aswhere the bend ends (i.e., on the other end from where the bend begins).In some embodiments of the present invention, a bend having non-zeroangle θ that is to be introduced in portion i is in the form of an arc.

If the bend having non-zero angle θ is to be introduced in portion i ofthermoplastic filament 131, then control of execution proceeds tooperation 604 for conditioning of portion i for bending. Otherwise,portion i to be deposited as a straight portion, and control ofexecution proceeds to operation 605.

In some embodiments of the present invention, control of executionproceeds to operation 604 based on angle θ exceeding a threshold that isa predetermined value greater than zero (e.g., π/36 radians, π/18radians, π/6 radians, etc.), wherein control of execution otherwiseproceeds to operation 605. In such embodiments, it might be determined,for example, that the conditioning that is performed in operation 604 isunnecessary for small bends. The threshold can be selected based on thethermoplastic filament being used or the object being manufactured, orboth, for example and without limitation.

Operation 604 is depicted in FIG. 6B. At operation 611, controller 101directs heating device 401 to add a first amount of heat to portion i ofthermoplastic filament 131 while being supplied for deposition, based ondetermining that the bend is to be introduced in said portion. Theadding of the first amount of heat is described above and in regard toFIG. 4.

At operation 612, controller directs twisting device 210 to twistportion i of the thermoplastic filament by a non-zero angle φ, after theadding of the first amount of heat in accordance with operation 611. Theamount of twist φ is described below and in regard to FIGS. 7 through10.

As those who are skilled in the art will appreciate after reading thisspecification, controller 101 can direct twisting device 210 to twistportion i either clockwise or counterclockwise, depending on one or moreconsiderations. Portion i can be twisted in a particular direction thatis based on, for example and without limitation, one or more of:

-   -   i. the direction of the curve to be applied to portion i, as        indicated in the computer model of object 151, and    -   ii. the direction(s) of the curves of one or more previous        portions, as indicated in the computer model of object 151, and    -   iii. the direction of the twist that was applied to the        preceding portion, or the direction(s) of the twists of one or        more previous portions, and    -   iv. the direction(s) of the curves to be applied to one or more        portions after portion i, as indicated in the computer model of        object 151, and    -   v. random choice.

At operation 613, portion i is cooled along cooling section 402, in amanner that is consistent with annealing of the thermoplastic. In someembodiments of the present invention, controller 101 controls thecooling process, as described above and in regard to FIG. 4.

Control of execution proceeds to operation 605, which is depicted inFIG. 6C. At operation 621, controller 101 directs laser 206 to add asecond amount of heat to portion i of thermoplastic filament 131 aftertwisting and/or cooling of the portion, wherein the second amount ofheat is sufficient make the portion pliable for deposition as discussedabove and in regard to FIG. 2.

At operation 622, controller 101 directs deposition head 122 to depositportion i of thermoplastic filament 131 on object 151, after thereheating that is performed at operation 621. The deposition head movesin relation to object 151 and according to the bend (e.g., curve to theleft, curve to the right, etc.), and deposits portion i according to themovement of the deposition head.

Control of execution proceeds to operation 606, in which portion counteri is incremented. At operation 607, controller 101 determines whetherthe I filament portions of the current segment have been processed. Ifall of the filament portions have not yet been processed, control ofexecution proceeds back to operation 603 in order to process the nextfilament portion. Otherwise, control of execution proceeds to theprocessing of the portions of the next segment of filament.

Controller 101 and the controlled components repeat operations 603 andhigher, for the next contiguous portion of thermoplastic filament 131and subsequent portions on the current segment, and for all portions onall subsequent segments after that. Multiple, contiguous portions ofthermoplastic filament are depicted in FIGS. 7 through 10, whichillustrate some examples of combinations of filament portions that makeup a filament segment. As those who are skilled in the art willappreciate after reading this specification, other combinations ofportions of thermoplastic filament are possible, in addition to thosethat are depicted and described below.

FIG. 7 depicts a side view of segment 701 of thermoplastic filament 131.Filament segment 701 is has a longitudinal axis L, denoted by axis 702in the figure, and is of length s as measured along longitudinal axis702. Segment 701 comprises reinforcing fibers (e.g., carbon fibers,etc.), including reinforcing fibers 703-a and 703-b whose relativepositions within segment 701 are superimposed on the segment as dottedlines. Fibers 703-a and 703-b are substantially parallel to longitudinalaxis 702. As described earlier, filament 131 can comprise thousands offibers, of which fibers 703-a and 703-b are but two of those fibers. Forclarity purposes, each of fibers 703-a and 703-b is depicted as beingsituated midway between longitudinal axis 702 and the lateral surface ofsegment 701.

FIG. 8 depicts a cross sectional view of segment 701 of thermoplasticfilament 131 in relation to longitudinal axis 702. Spatial relationshipsof the cross section of segment 701 in FIG. 8 to the side view in FIG. 7are represented by the x, y, and z coordinate notations in the twofigures. For clarity purposes, longitudinal axis 702, fiber 703-a, andfiber 703-b are depicted as being aligned with one another along thesame axis (the y-axis).

FIG. 9 depicts a first portion, a second portion, and a third portion ofsegment 701 of filament 131, which are denoted as portion 901,portion902,and portion 903, respectively. Portions 901, 902, and 903 havelengths S₁, S₂, and S₃, respectively (e.g., as measured along axis 702,etc.). One or more of lengths S₁, S₂, and S₃ can be different from oneanother, as those who are skilled in the art will appreciate afterreading this specification. In general, portions 901 through 903 aredeposited according to system 100 and method 600 disclosed herein.

Deposition head 122, while under the control of controller 101, depositsstraight portion 901 of segment 701 of thermoplastic filament 131 in astraight line without twisting filament 131 or the reinforcing fibers703-a and 703-b around longitudinal axis 702.

Deposition head 122 deposits arced portion 902 of segment 701 ofthermoplastic filament 131 in an arc of θ₁ radians and radius R₁ whiletwisting filament 131 and the reinforcing fibers 703-a and 703-b by theamount of φ₁ radians around longitudinal axis 702. Portions 901 and 902are contiguous with respect to each other. In some embodiments of thepresent invention,

$0 < \theta_{1} \leq \frac{\pi}{2}$

and φ₁=2πN₁, where N₁ is a non-zero integer. In some embodiments of thepresent invention, each of reinforcing fibers 703-a and 703-b inthermoplastic filament 131 in portion 902 forms a helix around a curvedportion of the longitudinal axis 702 with a rate of twist of

$\frac{d\; \phi_{1}}{{dS}_{2}} \neq 0$

such that

$\frac{d^{2}\phi_{1}}{{dS}_{2}^{2}} = 0.$

The rationale behind twisting the filament by the amount of φ₁=2πN₁,where N₁ is a non-zero integer, is based on the goal of exposing evenlyall of the fibers in the filament to all of the different forces—namely,compressive and tensile—that are applied as a result of bending theportion of filament. For example, this can be accomplished by twistingthe filament by 2π radians, which is equal to one complete rotation offilament 131. The rational behind maintaining a constant rate oftwist—namely, maintaining

$\frac{d^{2}\phi_{1}}{{dS}_{2}^{2}} = 0$

—furthers the aforementioned goal of exposing evenly all of the fibersto the applied forces that are related to bending the filament.

In some embodiments of the present invention, if θ₁ in arced portion 902exceeds a predetermined amount (e.g., π/2 radians, etc.), controller 101treats the arced portion as two or more arced sub-portions. Thesub-portions are identified such that the value for ϑ of each arcsub-portion does not exceed the predetermined amount, and the amount oftwist that is applied to each arced sub-position is equal to 2πN, whereN is a non-zero integer.

In some alternative embodiments of the present invention, and asdescribed earlier, deposition head 122 twists filament 131 and thereinforcing fibers 703-a and 703-b, only if angle θ exceeds a thresholdthat is a predetermined value greater than zero (e.g., π/36 radians,π/18 radians, π/6 radians, etc.). In some alternative embodiments of thepresent invention, deposition head 122 twists filament 131 and thereinforcing fibers 703-a and 703-b, only if the length of the arcedportion exceeds a predetermined, non-zero threshold.

Deposition head 122 deposits straight portion 903 of segment 701 ofthermoplastic filament 131 in a straight line without twisting filament131 or the reinforcing fibers 703-a and 703-b around longitudinal axis702. Portions 902 and 903 are contiguous with respect to each other.

FIG. 10 depicts a first straight portion, a first arced portion, asecond arced portion, and a second straight portion of segment 701 offilament 131, which are denoted as portion 1001, portion 1002, portion1003, and portion 1004 respectively. Portions 1001, 1002, 1003, and 1004have lengths S₁, S₂, S₃, and S₄, respectively (e.g., as measured alongaxis 702, etc.). One or more of lengths S₁, S₂, S₃, and S₄ can bedifferent from one another, as those who are skilled in the art willappreciate after reading this specification. In general, portions 1001through 1004 are deposited according to system 100 and method 600disclosed herein.

Deposition head 122, while under the control of controller 101, depositsportion 1001 of segment 701 of thermoplastic filament 131 in a straightline without twisting filament 131 or the reinforcing fibers 703-a and703-b around longitudinal axis 702.

Deposition head 122 deposits portion 1002 of segment 701 ofthermoplastic filament 131 in an arc of θ₁ radians and radius R₁ whiletwisting filament 131 and the reinforcing fibers 703-a and 703-b by theamount of φ₁ radians around longitudinal axis 702. Portions 1001 and1002 are contiguous with respect to each other. In some embodiments ofthe present invention,

$0 < \theta_{1} \leq \frac{\pi}{2}$

and φ₁=2πN₁, where N₁ is a non-zero integer. In some embodiments of thepresent invention, each of reinforcing fibers 703-a and 703-b inthermoplastic filament 131 in portion 1002 forms a helix around a curvedportion of the longitudinal axis 702 with a rate of twist of

$\frac{d\; \phi_{1}}{d\; S_{2}} \neq 0$

such that

$\frac{d^{2}\phi_{1}}{d\; S_{2}^{2}} = 0.$

Deposition head 122 deposits portion 1003 of segment 701 ofthermoplastic filament 131 in a second arc of θ₂ radians and radius R₂while twisting the thermoplastic filament and the reinforcing fibers703-a and 703-b by the amount of φ₂ radians around longitudinal axis702. Portions 1002 and 1003 are contiguous with respect to each other.In some embodiments of the present invention,

$0 < \theta_{2} \leq \frac{\pi}{2}$

and, φ₂=2πN₂, where N₂ is a non-zero integer.

As those are skilled in the art will appreciate after reading thisspecification, θ₁ and θ₂ can be either equal to or not equal to eachother; R₁ and R₂ can be either equal to or not equal to each other; R₁θ₁and R₂θ₂ can be either equal to or not equal to each other; and N₁ andN₂ can be either equal to or not equal to each other. In someembodiments of the present invention, each of reinforcing fibers 703-aand 703-b in portion 1003 forms a helix around a curved portion of thelongitudinal axis 702 with a rate of twist of

$\frac{d\; \phi_{1}}{d\; S_{3}} \neq 0$

such that

$\frac{d^{2}\phi_{1}}{d\; S_{3}^{2}} = 0.$

As depicted in FIG. 10, arced portion 1002 curves to the right and arcedportion 1003 curves to the left. As those who are skilled in the artwill appreciate after reading this specification, two contiguous arcedportions alternatively can both curve in the same direction, withsimilar treatment to that described above and for arced portions 1002and 1003 (i.e., twisting being administered on a per-arc basis). In somealternative embodiments of the present invention, however, controller101 can treat two contiguous arced portions both curving in samedirection as a single, combined arced portion of length S₁+S₂, based ona relationship between radius R₁ of the first arced portion and radiusR₂ of the second arced portion. For example, if values for R₁ and R₂ areless than a predetermined difference, controller 101 can treat the twocontiguous, arced portions as a combined arced portion, in thatdeposition head 122 twists filament 131 and the reinforcing fibers 703-aand 703-b by the amount φ₁=2πN across the combined arc, where N is anon-zero integer.

Deposition head 122 deposits portion 1004 of segment 701 ofthermoplastic filament 131 in a straight line without twisting filament131 or the reinforcing fibers 703-a and 703-b around longitudinal axis702. Portions 1003 and 1004 are contiguous with respect to each other.

In some embodiments of the present invention, a twisting of a portion ofa segment of filament 131 (e.g., arced portion 902,arced portion 1002,arced portion 1003, etc.) has the effect of causing enlargement in thethermoplastic toward the lateral surface of the portion. This is becausethe length of the reinforcing fibers, including fibers 703-a and 703-b,remain constant while they are twisted, resulting in the ends of thefilament portion along its longitudinal axis 702 moving towards eachother and thus causing the thermoplastic in the portion to movelaterally outward.

It is to be understood that the above-described embodiments are merelyillustrative of the present invention and that many variations of theabove-described embodiments can be devised by those skilled in the artwithout departing from the scope of the invention. It is thereforeintended that such variations be included within the scope of thefollowing claims and their equivalents.

What is claimed is:
 1. A method of depositing a thermoplastic filamentthat comprises (i) a longitudinal axis L and (ii) a reinforcing fiberthat is substantially parallel to the longitudinal axis L, the methodcomprising: depositing a first portion of a segment of the thermoplasticfilament in a straight line without twisting the thermoplastic filamentaround the longitudinal axis L and without twisting the reinforcingfiber around the longitudinal axis L, wherein the first straight portionof the segment has a length of S₁ as measured along the longitudinalaxis L; and depositing a second portion of the segment of thethermoplastic filament in a first arc of θ₁ radians and radius R₁ whiletwisting the second portion and the reinforcing fiber φ₁ radians aroundthe longitudinal axis L, wherein the second portion of the segment has alength of S₂ as measured along the longitudinal axis L; and depositing athird portion of the segment of the thermoplastic filament in a straightline without twisting the thermoplastic filament around the longitudinalaxis L and without twisting the reinforcing fiber around thelongitudinal axis L, wherein the third portion of the segment has alength of S₃ as measured along the longitudinal axis L; wherein thefirst portion of the segment and the second portion of the segment arecontiguous; and wherein the second portion of the segment and the thirdportion of the segment are contiguous; wherein S₁, S_(2,) S_(3,) and R₁are positive real numbers, and wherein θ₁ and φ₁ are real non-zeronumbers.
 2. The method of claim 1 wherein φ₁=2πN₁ where N₁ is a non-zerointeger.
 3. The method of claim 1 wherein φ₁=2π.
 4. The method of claim1 wherein the reinforcing fiber in the thermoplastic filament in thesecond portion of the segment has the form of a helix with a rate oftwist of $\frac{d\; \phi_{1}}{d\; S_{2}} \neq 0$ such that$\frac{d^{2}\phi_{1}}{d\; S_{2}^{2}} = 0.$
 5. A method of depositinga thermoplastic filament that comprises (i) a longitudinal axis L and(ii) a reinforcing fiber that is substantially parallel to thelongitudinal axis L, the method comprising: depositing a first portionof the segment of the thermoplastic filament in a first arc of θ₁radians and radius R₁ while twisting the first portion and thereinforcing fiber φ₁ radians around the longitudinal axis L, wherein thefirst portion of the segment has a length of S₁ as measured along thelongitudinal axis L; depositing a second portion of the segment of thethermoplastic filament in a straight line without twisting thethermoplastic filament around the longitudinal axis L and withouttwisting the reinforcing fiber around the longitudinal axis L, whereinthe second portion of the segment has a length of S₂ as measured alongthe longitudinal axis L; and depositing a third portion of the segmentof the thermoplastic filament in a second arc of θ₂ radians and radiusR2 while twisting the third portion and the reinforcing fiber φ₂ radiansaround the longitudinal axis L, wherein the third portion of the segmenthas a length of S₃ as measured along the longitudinal axis L; whereinthe first portion of the segment and the second portion of the segmentare contiguous; wherein the second portion of the segment and the thirdportion of the segment are contiguous; and wherein S₁, S_(2,) S_(3,) R₁,and R2 are positive real numbers, and wherein θ₁, θ_(2,) φ₁, and φ₂ arereal non-zero numbers.
 6. The method of claim 5 wherein φ₁=2πN₁ andφ₂=2πN₂, and wherein N₁ and N₂ are non-zero integers.
 7. The method ofclaim 6 wherein N₁=−N₂.
 8. The method of claim 6 wherein N₁=1 and N₂=−1.9. The method of claim 5 wherein θ₁≠θ₂ and φ₁=φ₂.
 10. The method ofclaim 5 wherein R₁≠R₂ and φ₁=φ₂.
 11. The method of claim 5 whereinR₁θ₁≠R₂θ₂ and φ₁=φ₂.
 12. The method of claim 5 wherein the reinforcingfiber in the thermoplastic filament in the second portion of the segmenthas the form of a helix with a rate of twist of$\frac{d\; \phi_{1}}{d\; S_{1}} \neq 0$ such that${\frac{d^{2}\phi_{1}}{d\; S_{1}^{2}} = 0};$ and wherein thereinforcing fiber in the thermoplastic filament in the third portion ofthe segment has the form of a helix with a rate of twist of$\frac{d\; \phi_{2}}{d\; S_{3}} \neq 0$ such that$\frac{d^{2}\phi_{2}}{d\; S_{3}^{2}} = 0.$
 13. A method of depositinga thermoplastic filament that comprises (i) a longitudinal axis L and(ii) a reinforcing fiber that is substantially parallel to thelongitudinal axis L, the method comprising: depositing a first portionof a segment of the thermoplastic filament in a first arc of θ₁ radiansand radius R ₁ while twisting the first portion and the reinforcingfiber φ₁ radians around the longitudinal axis L, wherein the firstportion of the segment has a length of S₁ as measured along thelongitudinal axis L; and depositing a second portion of the segment ofthe thermoplastic filament in a second arc of θ₂ radians and radius R₂while twisting the second portion and the reinforcing fiber φ₂ radiansaround the longitudinal axis L, wherein the second portion of thesegment has a length of S₂ as measured along the longitudinal axis L;wherein the first portion of the segment and the second portion of thesegment are contiguous; and wherein S₁, S_(2,) R_(1,) and R₂ arepositive real numbers, and wherein θ₁, θ_(2,) φ₁ and φ₂ are realnon-zero numbers.
 14. The method of claim 13 wherein φ₁ =2N₁ and φ₂=2N₂,and wherein N₁ and N₂ are non-zero integers.
 15. The method of claim 14wherein N₁=−N₂.
 16. The method of claim 14 wherein N₁=1 and N₂=−1. 17.The method of claim 13 wherein θ₁≠θ₂ and φ₁=φ₂.
 18. The method of claim13 wherein R₁≠R₂ and φ₁=φ₂.
 19. The method of claim 13 wherein R₁θ₁≠R₂θ₂and φ₁=φ₂.
 20. The method of claim 13 wherein the reinforcing fiber inthe thermoplastic filament in the first portion of the segment has theform of a helix around a curved portion of the longitudinal axis L witha rate of twist of $\frac{d\; \phi_{1}}{d\; S_{1}} \neq 0$ such that${\frac{d^{2}\phi_{1}}{d\; S_{1}^{2}} = 0};$ and wherein thereinforcing fiber in the thermoplastic filament in the second portion ofthe segment has the form of a helix around a curved portion of thelongitudinal axis L with a rate of twist of$\frac{d\; \phi_{2}}{d\; S_{2}} \neq 0$ such that$\frac{d^{2}\phi_{2}}{d\; S_{2}^{2}} = 0.$